This book is an introduction to topological dynamics and ergodic theory. It is divided into a number of relatively short chapters with the intention that each may be used as a component of a lecture course tailored to the particular audience. The authors provide a number of applications, principally to number theory and arithmetic progressions (through Van der Waerden's theorem and Szemerdi's theorem). This text is suitable for advanced undergraduate and beginning graduate students.
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' ... the volume achieves its goals well. It covers a broad range of topics clearly and succinctly ... There is much material here to interest and stimulate the reader ... I thoroughly recommend it to anyone of has some knowledge of the subject matter and wants a concise and well presented reference for more advanced concepts.' UK Non-Linear News
Book Description
This book is an essentially self contained introduction to topological dynamics and ergodic theory. It is divided into a number of relatively short chapters with the intention that each may be used as a component of a lecture course tailored to the particular audience. Parts of the book are suitable for a final year undergraduate course or for a masters level course. A number of applications are given, principally to number theory and arithmetic progressions (through van der waerden's theorem and szemerdi's theorem).
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This review is from: Dynamical Systems and Ergodic Theory (London Mathematical Society Student Texts) (Paperback)
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First Sentence:
In this chapter we shall introduce some of the basic dynamical properties associated to continuous maps T : X X on compact metric spaces. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
increasing martingale theorem, commuting homeomorphisms, hyperbolic toral automorphisms, measure theoretic entropy, topological entropy, recurrence theorem, ergodic measures, chain recurrent, prime period, ergodic theory, maximal cardinality, periodic point, ergodic theorem, measure preserving transformation, interval maps, weak mixing, compact metric space, shift map, finite cover, finite type Key Phrases - Capitalized Phrases (CAPs): (learn more)
New York, Lecture Notes, Chaotic Dynamical Systems, Modern Theory of Dynamical Systems New!
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Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
In this chapter we shall introduce some of the basic dynamical properties associated to continuous maps T : X X on compact metric spaces. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
increasing martingale theorem, commuting homeomorphisms, hyperbolic toral automorphisms, measure theoretic entropy, topological entropy, recurrence theorem, ergodic measures, chain recurrent, prime period, ergodic theory, maximal cardinality, periodic point, ergodic theorem, measure preserving transformation, interval maps, weak mixing, compact metric space, shift map, finite cover, finite type Key Phrases - Capitalized Phrases (CAPs): (learn more)
New York, Lecture Notes, Chaotic Dynamical Systems, Modern Theory of Dynamical Systems New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
Citations (learn more)
This book cites 19
books:
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9
books
cite this book:
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- Ergodic Theory (Cambridge Studies in Advanced Mathematics) by Karl E. Petersen on 6 pages
- An Introduction to Ergodic Theory (Graduate Texts in Mathematics) by Peter Walters on 6 pages
- Topics in Ergodic Theory (Cambridge Tracts in Mathematics) by William Parry on 4 pages
- An Introduction to Chaotic Dynamical Systems, 2nd Edition by Robert Devaney on 4 pages
- Introduction to the Modern Theory of Dynamical Systems (Encyclopedia of Mathematics and its Applications) by Anatole Katok on page 9, page 64, and page 71
See all 19 books this book cites
- Chaos and Chance: An Introduction to Stochastic Aspects of Dynamics by Arno Berger in Back Matter (1), and Back Matter (2)
- Chaos and Chance: An Introduction to Stochastic Aspects of Dynamics (de Gruyter Textbook) by Arno Berger in Back Matter (1), and Back Matter (2)
- Low-Dimensional Systems: Interactions and Transport Properties (Lecture Notes in Physics) (V. 544) by Tobias Brandes on page 21
- Computational Ergodic Theory (Algorithms and Computation in Mathematics) by Geon Ho Choe in Back Matter
- Fractal Dimensions for Poincare Recurrences, Volume 2 (Monograph Series on Nonlinear Science and Complexity) by Valentin Afraimovich in Back Matter
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